# Time Travel Not Ruled Out by the Laws of Physics

A closed timelike curve is a loop back in time (somewhat like the time portals in the Hollywood film Looper). That is, at certain "locations" in spacetime, there is a wormhole such that, if you jump in, you'll emerge at some point in the past. To the best of our knowledge, these time loops are not ruled out by the laws of physics.

Recent research of Todd Brun, Andreas Winter and I shows how a time traveler can copy quantum data at will, in violation of a fundamental principle of quantum mechanics often referred to as the "no quantum Xerox machine" theorem. The method involves looping a quantum particle back many times in the past and then reading out many copies of it in such a way that you don't disturb the past.

Backtracking a little bit, in 1991, David Deutsch, a theoretical physicist at Oxford University, came up with a model of time travel and quantum mechanics that resolves various time travel paradoxes that can arise (and which have often been depicted in Hollywood films such as Terminator, Looper, and Back to the Future).

There are two well known paradoxes:

1) First, the most famous is the "grandfather paradox," in which the time traveler goes back in time and kills her grandfather. If she is successful, how was she born in the first place to do so?

2) Second, we have the "Shakespeare paradox." That is, the time traveler reads the works of Shakespeare, writes them down in a book, and sends them back in time. Shakespeare then finds the book and writes everything down. Who wrote the works of Shakespeare in the first place?

An interesting aspect of Deutsch's model is that it allows for a time traveler to change the past, as long as she does so in a self-consistent manner. That is, a time traveler could kill her grandfather with probability one half, and then she wouldn't be born with probability one half, but the opposite possibility (her being born) is a fair chance with probability one half.

On the other hand, the no-cloning (or "no quantum Xerox machine") theorem is a fundamental tenet of quantum mechanics, the statement that it is impossible to produce a perfect copy of the state of an unknown quantum particle. Since it's easy to copy classical information and we do it all the time, it might seem a bit counterintuitive at first that copying quantum information is impossible. However, this theorem is at the heart of our understanding of quantum information and it represents one of the main physical reasons why quantum cryptography is secure.

What Todd Brun, Andreas Winter, and I recently showed is that, if these time loops behave according to Deutsch's model, then it would be possible to produce copies of quantum states at will, which is a violation of the no-cloning theorem discussed above. We first realized that we could create many copies of a quantum particle simply by sending it back into the past many times. You could then attempt to read out many copies of the particle, but if you do so, you'll disturb the past! So the main innovation was to figure out what to do to the quantum particle before sending it back many times into the past. After figuring that out, we realized we could send the particle back many times into the past and then read out many copies of it while not disturbing the past (so that no one there would notice the difference).

This ability to copy quantum information freely would turn quantum theory into an effectively classical theory in which, for example, classical data thought to be secured by quantum cryptography would no longer be safe. A malicious time looper could take advantage of this device to break quantum secured communications, potentially leading to catastrophic consequences.

Since the ability to copy quantum information freely is a strong violation of our beliefs about what should be possible in the physical world, we think our work serves as evidence against Deutsch's model. That is, it seems as if there should be a revision to Deutsch's model which would simultaneously resolve the various time travel paradoxes but not lead to such striking consequences for quantum information processing. However, no one yet has offered a model that meets these two requirements. This is the subject of open research!

Mark Wilde is Assistant Professor in the Physics and Astronomy Department at LSU.